Optimal. Leaf size=28 \[ x (a B+A b)-\frac{a A}{2 x^2}+\frac{1}{4} b B x^4 \]
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Rubi [A] time = 0.0159127, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {448} \[ x (a B+A b)-\frac{a A}{2 x^2}+\frac{1}{4} b B x^4 \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right ) \left (A+B x^3\right )}{x^3} \, dx &=\int \left (A b \left (1+\frac{a B}{A b}\right )+\frac{a A}{x^3}+b B x^3\right ) \, dx\\ &=-\frac{a A}{2 x^2}+(A b+a B) x+\frac{1}{4} b B x^4\\ \end{align*}
Mathematica [A] time = 0.0086834, size = 28, normalized size = 1. \[ x (a B+A b)-\frac{a A}{2 x^2}+\frac{1}{4} b B x^4 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 24, normalized size = 0.9 \begin{align*}{\frac{bB{x}^{4}}{4}}+Abx+Bax-{\frac{Aa}{2\,{x}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.26629, size = 32, normalized size = 1.14 \begin{align*} \frac{1}{4} \, B b x^{4} +{\left (B a + A b\right )} x - \frac{A a}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.38094, size = 63, normalized size = 2.25 \begin{align*} \frac{B b x^{6} + 4 \,{\left (B a + A b\right )} x^{3} - 2 \, A a}{4 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.258407, size = 24, normalized size = 0.86 \begin{align*} - \frac{A a}{2 x^{2}} + \frac{B b x^{4}}{4} + x \left (A b + B a\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15505, size = 31, normalized size = 1.11 \begin{align*} \frac{1}{4} \, B b x^{4} + B a x + A b x - \frac{A a}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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